North-South dynamics of hyperbolic free group automorphisms on the space of currents

Martin Lustig (1) , Caglar Uyanik

1 I2M - Institut de Mathématiques de Marseille

Let phi be a hyperbolic outer automorphism of a non-abelian free group F-N such that phi and phi(-1) admit absolute train track representatives. We prove that phi acts on the space of projectivized geodesic currents on F-N with generalized uniform North-South dynamics.

Domaines: Théorie des groupes [math.GR]

Martin Lustig, Caglar Uyanik. North-South dynamics of hyperbolic free group automorphisms on the space of currents. Journal of Topology and Analysis, 2019, 11 (2), pp.427-466. ⟨10.1142/S1793525319500201⟩. ⟨hal-03584056⟩